This is a puzzle.
Imagine I have three rods of length 1 each, and they are connected together with perfect hinges. Together, they form a somewhat flexible shape ABCD (with AB=1, BC=1 and CD=1), even if I fix the two ends A and D to the floor at a given distance k apart. The figure below shows examples for k=0, k=1, and k=2.
For each of these, we assume that A is at (0,0) and that D is at (k,0). For k=3, all flexibility disappears and there is only a single arrangement. For any value of k, we can look at the relationship between the height of hinge B and the height of hinge C. For some values of k, this relationship is simple; for others, the relationship is more involved.
For what values of k can you give a quantitative description of the relationship between the height of B and the height of C? Can you sketch a graph, derive a formula, give an analysis? I suggest you start with k=1, but don’t stop there!